Ergodic Theory and Diffusion Theory

Abstract

These theories constitute fascinating fields of application of the analytical theory of semi-groups. Mathematically speaking, the ergodic theory is concerned with the “time average” \(\mathop {\lim }\limits_{t \uparrow \infty } {t^{ - 1}}\int\limits_0^t {{T_s}}\)ds of a semi-group Tt, and the diffusion theory is concerned with the investigation of a stochastic process in terms of the infinitesimal generator of the semi-group intrinsically associated with the stochastic process.